
// Make newform 429.2.m.a in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_429_m();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_429_2_m_a();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_429_m();"
function MakeCharacter_429_m()
    N := 429;
    order := 4;
    char_gens := [287, 79, 67];
    v := [4, 2, 3];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_429_m_Hecke(Kf)
    return MakeCharacter_429_m();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_429_2_m_a();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_429_2_m_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_429_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, 0, 0, 0, 575, 0, 0, 0, 65769, 0, 0, 0, 82143, 0, 0, 0, 25707, 0, 0, 0, 2857, 0, 0, 0, 99, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;